2021 NJC Lecture Test

2. The diagram below shows a sketch of the curve with equation \(y=\mathrm{g}(x)\). The curve has asymptotes with equations\(x=0\) and \(y=2\). The curve crosses the \(x\)-axis at \(A(2,0)\) and \(C(7,0)\) and has a turning point at \(B(4,-2)\).
   
   On separate diagrams, sketch the curves with equations
   1. \(y=\left| \mathrm{g}(-x) \right|\),[3]
   2. \(y=\frac{1}{\mathrm{g}(x)}\).[4]

For each curve, state clearly the equations of any asymptotes, the coordinates of any turning points and the coordinates of any points where the curves crosses the \(x\)- and \(y\)- axes.